George Osborne is adopting a crafty approach to European plans for a new tax on financial transactions. The big four eurozone countries – Germany, France, Italy and Spain – are now all in favour of a levy and the chancellor's response is to let them get on with it.

Britain could have cut up rough about a so-called Tobin tax, but Osborne has decided that the aggro is not worth it. His assumption is that a financial transaction tax (FTT) will raise costs in Frankfurt, Paris, Milan and Madrid, and so drive business to the City.

The chancellor is also dubious about claims that the money will be spent on "good causes" such as development aid or helping poor countries adapt to climate change. In the event that an FTT does prove to be a cash cow, Osborne thinks hard-up European governments will use it to reduce their budget deficits.

From a narrow political perspective, the chancellor's stance makes sense. If the City prospers as a result of being a cheaper place to do business than rival financial centres in Europe, then London and the south-east will benefit. This will make it harder for Labour to win the swing seats in the home counties that it needs to form a government.

Critics of the FTT say that Osborne's approach is good economics as well as good politics. The Robin Hood tax is nothing of the sort, they say. Banks will pass the levy on to their customers and it will make it more expensive for exporters to hedge against currency movements and for homebuyers to get a mortgage.

The notion that the Robin Hood tax is actually a Sheriff of Nottingham tax cuts little ice with those European governments now planning to press on with the idea. They acknowledge that there will be what economists call behavioural effects from an FTT – some transactions will no longer happen as a result of the levy – but they are confident that the overall tax take will increase as a result. Revenue has to be raised from somewhere, so better that it come from the reviled financial sector than, say, raising income tax or VAT. The principle goes back to the 18th century French finance minister Jean-Baptiste Colbert, who said the "art of taxation consists in so plucking the goose as to obtain the largest amount of feathers with the smallest possible amount of hissing".

At the very least, an interesting experiment is now in prospect. If FTT supporters in Europe are right, the UK government will soon be looking enviously across the English Channel at all the lovely, easy wonga being raised in Germany and France. If there is an exodus of finance and financiers to Canary Wharf and Mayfair, Osborne will be able to say: "I told you so."

In one respect, however, the chancellor will be a loser whatever happens. One of the avowed aims of the government is to rebalance the economy, both from finance to manufacturing and from south to north. This is an entirely laudable and sensible objective, but desperately hard to achieve and not at all consistent with policies designed to reinforce the City's already considerable competitive edge.

A recent paper entitled Spatially Unbalanced Growth in the British Economy, by the Cambridge academics Ben Gardiner, Ron Martin and Peter Tyler, details how the north-south divide has widened as a result of two factors: the hollowing out of manufacturing and the rise of the post-big bang City. "Whilst financial services have grown in every region over the past four decades, the south has witnessed by far the most rapid increase, more than quadrupling real output from this part of the economy."

The study notes that in 1971 the south accounted for 56% of national output in financial and business services. By 2008 this had risen to 67%. So, while there are regional centres of strength in financial services, such as Leeds and Edinburgh, London's dominance has increased.

One strand of economic theory holds that market forces will even out these imbalances. Rising output and employment in the south will lead to pressure on resources and higher costs in financial services. Businesses will then move to the north and set up businesses in sectors such as manufacturing where costs are lower.

It is hard, however, to square this theory with the facts. Stronger growth in London and the south-east has acted like a magnet, attracting investment and sucking talent out of the northern regions of the UK. Britain has a comparative advantage in financial services, and there has been a cluster effect. The Cambridge paper estimates that the northern regions would be £43bn richer had they grown at the same rate as the national economy between 1972 and 2010.

If anything, the financial crisis of the past five years has made the imbalances worse. It was manufacturing rather than finance that suffered most from the recession, and the north is more dependent on manufacturing than London and the south-east. The north suffered most in the economy's initial deep slump, gained least during the short-lived recovery and was first to feel the pain of a double-dip recession. Austerity is hitting the region hardest, because almost all the employment growth in recent years has been in the public sector.

If the Treasury is right in its realpolitik calculation that the City stands to gain from an FTT in large chunks of the eurozone, this will make the imbalances in the economy worse rather than better. It could be argued that encouraging trading in complex derivatives will increase the size of the financial sector, generating higher tax receipts which can be recycled into higher public spending in the poorer regions. This, though, was, precisely what happened in the years before the crisis. As a model it proved unsustainable.

Vince Cable made the case last week for an interventionist approach to house building, noting correctly that one of the big factors that helped Britain out of the slump in the 1930s was a private-sector construction boom. The business secretary proposed using the public sector balance sheet to leverage in private capital to the housing sector. This makes sense, especially at a time when interest rates on government borrowing are so low, but any expansion of housing supply would inevitably be skewed to London and the Home Counties, where demand is strongest.

The Cambridge paper argues that there is an urgent need for a clearly identified industrial policy in tandem with a regional policy to address the north-south divide. But the ideas floated – a national investment bank, a much-expanded regional growth fund, impact investment funds to promote advanced manufacturing – will all cost money at a time when Osborne is counting the pennies.

One argument that could be deployed by FTT supporters is that it would help make the financial sector less prone to speculative bubbles while generating a steady flow of income to be used to finance economic rebalancing. At least one half of the coalition might find such a prospect enticing.